Solving exponential simultaneous equations

The actual problem shows a graph however I can state all the information. The graph is of a sinusiodal waveform where the amplitude is decaying exponentially. The formula for the graph is given by the equation:

T = Ae^-Ktsin(wt + ø)

The question is to find A,K,w and ø

Being quite confident in sinusoidal waveforms I can tell you that:

w = 40 x pi or 125.66 (whichever tickles your fancy)
ø = -1.885

However im stuck with the A and K.

Assuming that the maximum peaks occur when sin(wt + ø) = 1 then:

0.23 = Ae^-K0.0275

0.08 = Ae^-K0.0775

I now have 2 points to solve simultaneously for A and K.

Heres my attempt:

0.23/0.08 = Ae^-K0.0275/Ae^-K0.0775

2.875 = e^-K0.5

K = (1/0.5) x ln(2.875) = 2.1121

When you plug this back into the two equations however you get two different answers for A and A is supposed to be a constant!! Can anyone see where im going wrong here?